"It was a pretty surreal feeling," Tufani, 24, said of the performance. "To hear someone sing with my mother’s lungs, it was something that I would’ve wanted to do if she was still here."

Tillemann-Dick's career was almost thwarted after being diagnosed in summer of 2004 with idiopathic pulmonary hypertension, a rare disease that can lead to heart failure and death.

"I went to the doctor for a routine check-up," Tillemann-Dick recalled. "And I left with her telling me ... that I had a life expectancy of two to five years. I just started laughing. It was just so tragic ... I locked myself in the bathroom and I had a good cry."

Charity Tillemann-Dick, an opera singer, recovering from her second double-lung transplant in January 2012.

Tillemann-Dick had to wait five years for her first double-lung transplant. It was welcome news since the opera singer said her health had taken a dramatic decline after the 2008 deaths of both her father, Timber Dick, from a car crash, and her grandfather, Tom Lantos, who passed away after battling cancer.

But the transplant was unsuccessful after her body rejected her new lungs, causing her to need a second transplant in 2012.

It was thanks to Tufani's estranged mother, Flora Brown, that Tillemann-Dick was able to have the rare surgery a second time around.

Falling in love with song

Tillemann-Dick remembers exactly when she fell in love with opera.

She was 5 years old when her sister's best friend took them to see a local production of Engelbert Humperdinck's opera "Hansel and Gretel."

"I remember sitting in the audience and being hit by this wall of sound. It was like a wave coming over me, a baptism by music," she recalled. "It was an early love affair, which has lasted a long time."

Tillemann-Dick, who had sung in her church's choir since the age of 3, formally began training by age 13. She would later be accepted into the Franz Liszt Academy of Music in Budapest, Hungary, where she trained for a year.

There, she became comfortable with her voice, she said.

Cleveland Clinic

Opera singer Charity Tillemann-Dick recovering from her second double-lung transplant in January 2012, along with her brother Zenith Tillemann-Dick and her husband Yonatan Doron.

"My voice always seemed too big for the occasion. It was always bigger than my peers. It just seemed a little out of place," she said. "But now it felt like it was exactly where it belonged because it had everything it needed to just fill a space."

Still, her body was failing her. As the months went by in 2004, her symptoms worsened. She'd often faint while crossing the street and twice while dancing, she recalled, noting that "physical activity was becoming increasingly difficult."

Tillemann-Dick, who recently penned a memoir called "The Encore" about her experience, felt a strange gratefulness for her diagnosis, which came the same year.

"On the one hand, it was devastating, and on the other hand it was relief," she explained. "When I got this diagnosis it was like, "Oh, I’m not imagining this ... there really is something that’s wrong."

A performance of a lifetime

The clinic that brought Tillemann-Dick and Tufani together invited them to share the stage to perform a duet last Tuesday at the Cleveland Clinic’s 15th annual Medical Innovation Summit in Ohio.

The opera singer, who performed with the lungs of Tufani's late mother, an immigrant from Honduras, helped Tufani feel comfortable onstage. The 24-year-old, who's a manager at a local Chipotle, is an aspiring singer, but is more comfortable performing at her local church.

The duo performed two of Tillemann-Dick's songs -- "Simple Grace" and "American Rainbow." The songs had much significance as the lyrics reflected the unique experience.

Tillemann-Dick said that while "Simple Grace" reminds people to not take life for granted, "American Rainbow" promotes a message of inclusivity.

"It feels like there’s a lot of discord in the world right now and in our own country," Tillemann-Dick said. "We forget our strength is what everyone brings to the table and all of these different voices."

"In my case, they’re what gave me life. I am alive because of an immigrant who came to this country in search of a better life, in search of hope," she said.

The performance touched many in the audience, including Tillemann-Dick's transplant doctor, Dr. Marie Budev, a pulmonologist who serves as the medical director of Cleveland Clinic's Lung Transplant Program.

"I've seen her perform several times now and each time I’m amazed. This time was very special," Dr. Budev told ABC News. "It was a very unique situation you don’t get to see that often."